Discordance between mean glucose and time in range in relation to HbA1c in individuals with type 1 diabetes: results from the GOLD and SILVER trials

Aims/hypothesis Previous studies have shown that individuals with similar mean glucose levels (MG) or percentage of time in range (TIR) may have different HbA1c values. The aim of this study was to further elucidate how MG and TIR are associated with HbA1c. Methods Data from the randomised clinical GOLD trial (n=144) and the follow-up SILVER trial (n=98) of adults with type 1 diabetes followed for 2.5 years were analysed. A total of 596 paired HbA1c/continuous glucose monitoring measurements were included. Linear mixed-effects models were used to account for intra-individual correlations in repeated-measures data. Results In the GOLD trial, the mean age of the participants (± SD) was 44±13 years, 63 (44%) were female, and the mean HbA1c (± SD) was 72±9.8 mmol/mol (8.7±0.9%). When correlating MG with HbA1c, MG explained 63% of the variation in HbA1c (r=0.79, p<0.001). The variation in HbA1c explained by MG increased to 88% (r=0.94, p value for improvement of fit <0.001) when accounting for person-to-person variation in the MG–HbA1c relationship. Time below range (TBR; <3.9 mmol/l), time above range (TAR) level 2 (>13.9 mmol/l) and glycaemic variability had little or no effect on the association. For a given MG and TIR, the HbA1c of 10% of individuals deviated by >8 mmol/mol (0.8%) from their estimated HbA1c based on the overall association between MG and TIR with HbA1c. TBR and TAR level 2 significantly influenced the association between TIR and HbA1c. At a given TIR, each 1% increase in TBR was related to a 0.6 mmol/mol lower HbA1c (95% CI 0.4, 0.9; p<0.001), and each 2% increase in TAR level 2 was related to a 0.4 mmol/mol higher HbA1c (95% CI 0.1, 0.6; p=0.003). However, neither TIR, TBR nor TAR level 2 were significantly associated with HbA1c when accounting for MG. Conclusions/interpretation Inter-individual variations exist between MG and HbA1c, as well as between TIR and HbA1c, with clinically important deviations in relatively large groups of individuals with type 1 diabetes. These results may provide important information to both healthcare providers and individuals with diabetes in terms of prognosis and when making diabetes management decisions. Graphical Abstract Supplementary Information The online version of this article (10.1007/s00125-024-06151-2) contains peer-reviewed but unedited supplementary material.


ESM Methods: Additional statistical analysis details
We evaluated possible time-dependent and non-linear and associations between blood glucose and HbA1c by correlating HbA1c to a weighted mean glucose metric depending on i) time of day, ii) time since the glucose value was attained, and iii) actual glucose value, as further detailed below.

Time of the day
The weighted mean glucose metric was calculated as where   is the mean glucose during daytime (06:00-22:00),  ℎ the mean glucose during nighttime (22:00-06:00), and  ∈ [0, 1] a weight parameter to be estimated.The optimal weight  � was estimated by maximising the log-likelihood of the random intercepts model where 1  is the observed HbA1c for individual  at visit ,   the corresponding weighted mean glucose metric,   a subject-specific random intercept, and   a random (residual) error.The random intercepts and residual errors were assumed to be uncorrelated and normally distributed with zero mean.The null hypothesis that  = 2/3, i.e., that measurements obtained during daytime and nighttime contribute equally to the association with HbA1c ( = 2/3 ⇔ 16 hours daytime divided by 24), was tested using a likelihood ratio test.
Similar calculations were performed for time in range.

Time since the glucose value was attained
The weighted mean glucose metric was calculated as where () =  − is an exponential weight function,  the time since the glucose value was attained, () the observed glucose value at timepoint , and  an exponential decay parameter to be estimated.The constant  was chosen for each subject and visit so that ∑ ()  = 1, with summation over all timepoints for which a glucose measurement was available.The optimal parameter  � was estimated by maximising the log-likelihood of the random intercepts model (1) as a function of the coefficient .The null hypothesis that  = 0, i.e., that all glucose measurements contribute equally to the association with HbA1c, was tested using a likelihood ratio test.Similar calculations were performed for time in range.

Distribution of glucose values
The weighted mean glucose metric was calculated as , where 2.22 and 22.2 is the lower and upper measurement limit of the CGM device,  the glucose value, () a weight function, and () a probability measure for the distribution of glucose values.The probability measure () was taken as the empirical measure, i.e., the relative frequency of glucose values.Values <2.22 mmol/l were taken as 2.22 mmol/l and values ≥22.2 mmol/l taken as 22.2 mmol/l.The weight function () was modelled using fractional polynomials, i.e., as a function on the form (2) To avoid overfitting, some of the coefficients   were set to zero.The best fitting fractional polynomial for the random intercepts model (1) was selected using best subset selection of all fractional polynomials including at most three terms by minimising the Akaike Information Criterion (AIC).
Combining (1) and (2), the model form the mean HbA1c related to the distribution of blood glucose can also be written on the form We note that a linear model corresponds to a linear relationship between mean glucose and HbA1c.Statistical analyses were performed using linear mixed effects models.Percentage time in range and one covariate at a time were included as fixed effects.Subject-specific random intercepts were included as random effects to account for inter-individual deviations from the mean trend and intra-individual correlations in repeated-measures data.*The covariate was log-transformed prior to analysis.The regression coefficient represents the expected change in HbA 1c per 50% increase in the covariate.#Not significant when accounting for time below range (<3.9 mmol/l) and time above range level 2 (>13.9 mmol/l).Abbreviations: APOA1, apolipoprotein A1; APOB, apolipoprotein B; BMI, body mass index; CGM, continuous glucose monitoring; CI, confidence interval; CRP, C-reactive protein; CV, coefficient of variation; DTSQ, diabetes treatment satisfaction questionnaire; HCS, hypoglycaemia confidence scale; HDL, high density lipoprotein; LDL, low density lipoprotein; MAGE, mean amplitude of glycaemic excursions; SD, standard deviation; TIR, time in range.4. Interaction analyses relating HbA1c (mmol/mol) to time in range (TIR, 3.9-10.0mmol/l), glycaemic variability measures, time in glycaemic ranges, patient characteristics, and baseline covariates.Results are presented as regression coefficients with 95% confidence intervals.The interaction effect represents the interaction between TIR and the covariate.Statistical analyses were performed using linear mixed effects models.Percentage time in range, covariate, and covariate with CGM mean interaction were included as fixed effects.Subject-specific random intercepts were included as random effects to account for inter-individual deviations from the mean trend and intra-individual correlations in repeated-measures data.*The covariate was log-transformed prior to analysis.The regression coefficient represents the expected change in HbA 1c per 50% increase in the covariate.#Not significant when accounting for time below range (<3.9 mmol/l) and time above range level 2 (>13.9 mmol/l).Abbreviations: APOA1, apolipoprotein A1; APOB, apolipoprotein B; BMI, body mass index; CGM, continuous glucose monitoring; CI, confidence interval; CRP, C-reactive protein; CV, coefficient of variation; DTSQ, diabetes treatment satisfaction questionnaire; HCS, hypoglycaemia confidence scale; HDL, high density lipoprotein; LDL, low density lipoprotein; MAGE, mean amplitude of glycaemic excursions; SD, standard deviation; TIR, time in range.

ESM Table
ESM Figure 1.Non-linear association between HbA1c and the distribution of glucose values derived on data from the GOLD trial (n=144).The estimated HbA1c (eA1c) is expressed as a weighted sum (integral) of the individual glucose values (x) with weight function β(x).dP(x) is a probability measure, i.e., the relative frequency or density of glucose values.A linear weight function corresponds to a linear relationship between HbA1c and MG (cf. Figure 1).The weight function was determined by best subset selection (minimise Akaike's Information Criterion) on all fractional polynomial models with up to three parameters.
ESM Figure 2. Non-linear association between HbA1c and the distribution of glucose values validated on data from the SILVER trial (n=98).The estimated HbA1c (eA1c) is expressed as a weighted sum (integral) of the individual glucose values (x) with weight function β(x).dP(x) is a probability measure, i.e., the relative frequency or density of glucose values.A linear weight function corresponds to a linear relationship between HbA1c and MG (cf. Figure 1).The same fractional polynomial weight function as in Figure S1 was used and re-fitted on data from the SILVER study.

Table 3 .
Linear mixed-effects regression models relating

Table 1 .
Linear mixed-effects regression models relating HbA1c (mmol/mol) to mean glucose (mmol/l), glycaemic variability measures, time in glycaemic ranges, patient characteristics, and baseline covariates.Results are presented as regression coefficients with 95% confidence intervals.

Table 2 .
Interaction analyses relating HbA1c (mmol/mol) to mean glucose (mmol/l), glycaemic variability measures, time in glycaemic ranges, patient characteristics, and baseline covariates.Results are presented as regression coefficients with 95% confidence intervals.The interaction effect represents the interaction between mean glucose and the covariate.
Statistical analyses were performed using linear mixed effects models.CGM mean, covariate, and covariate with CGM mean interaction were included as fixed effects.Subject-specific random intercepts were included as random effects to account for inter-individual deviations from the mean trend and intra-individual correlations in repeated-measures data.*Thecovariate was log-transformed prior to analysis.The regression coefficient represents the expected change in HbA 1c per 50% increase in the covariate.Abbreviations: APOA1, apolipoprotein A1; APOB, apolipoprotein B; BMI, body mass index; CGM, continuous glucose monitoring; CI, confidence interval; CRP, C-reactive protein; CV, coefficient of variation; DTSQ, diabetes treatment satisfaction questionnaire; HCS, hypoglycaemia confidence scale; HDL, high density lipoprotein; LDL, low density lipoprotein; MAGE, mean amplitude of glycaemic excursions; SD, standard deviation.ESM

Table 3 .
Linear mixed-effects regression models relating HbA1c (mmol/mol) to time in range (TIR, 3.9-10.0mmol/l), glycaemic variability measures, time in glycaemic ranges, patient characteristics, and baseline covariates.Results are presented as regression coefficients with 95% confidence intervals.